M361K: Introduction to Real Analysis, Autumn 2012

Unique ID

56225

Course time

MWF 1:00–2:00 PM

Course location

RLM 7.124

Instructor

Samuel Isaacson

Office

RLM 11.164

Office hours

• Wednesday, 2:30–4:00 PM
• Thursday, 1:30–3:00 PM
• By appointment

Email

isaacson@math.utexas.edu

Textbook

Bartle, Robert G. and Sherbert, Donald R. Introduction to Real Analysis. 4th ed. Hoboken, NJ: John Wiley & Sons, Inc., 2011.

Prerequisites

This course requires consent of the undergraduate advisor or two of the following courses with a grade of at least C− in each: M325K or Philosophy 313K, M328K, M341.

Antirequisites

You may not take M361K if you have received a grade of C− or higher in M365K.

Homework

There will be 5 homework assignments; see the homework policy below.

Midterm exams

• Friday, September 28, during lecture
• Friday, October 26, during lecture

Final exam time

Wednesday, December 12, 9:00 AM–12:00 PM

Final exam location

RLM 7.124

Evaluation

• Homework: 20%
• Midterms: 30% (each is worth 15%)
• Final exam: 50%

Grade scale

This scale is subject to revision.

A	93–100	C	73–76
A−	90–92	C−	70–72
B+	87–89	D+	67–69
B	83–86	D	63–66
B−	80–82	D−	60–62
C+	77–79	F	0–59

Attendance

Attendance is recommended but not required.

Course description

M361K is a mathematically rigorous introduction to real analysis. The course topics include the definition and topology of the real line, continuity, differentiation, and the Riemann-Stieltjes integral.

Textbook

The following textbook is required:

1. Bartle, Robert G. and Sherbert, Donald R. Introduction to Real Analysis. 4th ed. Hoboken, NJ: John Wiley & Sons, Inc., 2011.

Bartle and Sherbert is available on reserve at the Kuehne Physics-Math-Astronomy library. I also recommend the following optional books:

2. Gelbaum, Bernard R., and Olmsted, John M. H. Counterexamples in Analysis. New York: Dover Publications, 2003.

3. Kolmogorov, Andrey N., and Fomin, Sergei V. Elements of the Theory of Real and Functional Analysis. Translated by Leo F. Boron, Hyman Kamel, and Horace Komm. New York: Dover Publications, 1999.

4. Kolmogorov, Andrey N., and Fomin, Sergei V. Introductory Real Analysis. Translated and edited by Richard A. Silverman. New York: Dover Publications, 1970.

5. Körner, Thomas W. A Companion to Analysis: A Second First and First Second Course in Analysis. Providence, RI: American Mathematical Society, 2004.

6. Körner, Thomas W. Exercises in Fourier Analysis. Cambridge: Cambridge University Press, 1993.

7. Körner, Thomas W. Fourier Analysis. Cambridge: Cambridge University Press, 1988.

8. Lakeland, Grant, et al. Introduction to Real Analysis: M361K. University of Texas course notes, available online, last modified July 2011.

9. Rudin, Walter. Principles of Mathematical Analysis. 3rd ed. New York: McGraw-Hill, Inc., 1976.

10. Sally, Paul. Tools of the Trade: Introduction to Advanced Mathematics. Providence, RI: American Mathematical Society, 2008.

11. Steele, J. Michael. The Cauchy-Schwarz Master Class: An Introduction to the Art of Mathematical Inequalities. Cambridge: Cambridge University Press, 2004.

Homework

Problem sets are worth 20% of your grade. There will be five assignments due over the course of the semester. Homework will be collected at the beginning of lectures. Late homework will not be accepted.

I encourage you to work with other students on homework problems. However, your homework must be in your own words. Write up your homework by yourself; if you worked with anyone on the homework, you must indicate so. See the note below on academic integrity.

Exams

In addition to the final exam, there will be two midterm exams during the semester whose dates are noted above. The midterms will be administered during lectures. The midterms and final are worth 80% of your grade with each midterm worth 15% and the final worth 50%. The final will be cumulative.

Calculators and notes will not be permitted on exams. Bring your UT ID with you to each exam.

If you cannot write an exam, let me know at least two weeks in advance. For each exam, there will be a make-up offered for students who missed the original due to an excused absence or medical emergency. If you cannot write the make-up exam, the exam will be dropped.

Email

If you need to email me regarding this course, please include your EID and the unique number of this course. I will not discuss grades over email.

Religious holidays

In accordance with UT Austin policy, please notify me at least 14 days prior to the date of observance of a religious holiday. If the holiday conflicts with an exam, I will allow you to write a make-up exam within a reasonable time.

Special needs

Students with disabilities may request appropriate academic accommodations from the Division of Diversity and Community Engagement, Services for Students with Disabilities at 471-6259 (voice), 232-2937 (video), or http://www.utexas.edu/diversity/ddce/ssd.

Academic integrity

If you work with other students, indicate so on your homework. There is no penalty for working with other students, but you must write up your homework by yourself. You may use a calculator or computer system such as Sage or MATLAB on your homework, but calculators and computers are forbidden on exams. Read the University’s standard on academic integrity found on the Student Judicial Services website.

Electronic course instructor survey

Electronic course instructor surveys (eCIS) will be available for the last two weeks of the semester. During the survey period, you may fill out eCIS on UT Direct.

Course plan and lecture notes

This plan may change as the semester progresses. Lecture notes will be posted periodically.

Important dates